As outlined in Section 3.2, our adaptation of the two-step GFPCA approach of [1]} is based on
an additive regression model with random intercept terms for the
individual FPCs.
We build on robust and highly efficient software for these kinds of models,
available in packages gamm4 [2]} and lme4 [3]}.
The algorithms of lme4 are highly efficient for estimating models
with random intercept terms with several thousand individual categories.
The estimation of the marginal mean of the process \(X_i(t)\) 
in the case of very large data with \(>100\,000\)  rows is performed with the discretization-based estimation algorithm of function mgcv::bam
[4]} rather than the estimation algorithm of mgcv::gam
[5]}.
